Summability of double independent random variables

We will examine double sequence to double sequence transformation of independent identically distribution random variables with respect to four-dimensional summability matrix methods. The main goal of this paper is the presentation of the following theorem. If max(k,l)vertical bar a(m,n,k,l) vertical bar = max(k,l)vertical bar a(m,k)a(n,l)vertical bar = O(m(-gamma 1))O(n(-gamma 2)) gamma(1),gamma(2) > 0, then E vertical bar X vertical bar(1+1/gamma 1) < infinity and E vertical bar X vertical bar(1+1/gamma 2) < infinity imply that Y-m,Y-n -> mu almost sure P- convergence.